SOLUTION: (a) Find the mean and variance of the random variable X having the following probability distribution: X 1 0 2.1 3.1 P(X = x) 0.3 0.4 0.1 0.2 b)Let X be disc

Algebra ->  Probability-and-statistics -> SOLUTION: (a) Find the mean and variance of the random variable X having the following probability distribution: X 1 0 2.1 3.1 P(X = x) 0.3 0.4 0.1 0.2 b)Let X be disc      Log On


   

Question 891689: (a) Find the mean and variance of the random variable X having the following probability distribution:
X 1 0 2.1 3.1
P(X = x) 0.3 0.4 0.1 0.2

b)Let X be discrete random variable having Poisson distribution. If P( X = 0) = 0.264, find p (X = 1)&p(X >2).
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(b) The pmf for the poisson distribution is
p%28x%29+=+%28lambda%5Ex%2Fx%21%29%2Ae%5E%28-lambda%29
p%280%29+=+%28lambda%5E0%2F0%21%29%2Ae%5E%28-lambda%29+=+0.264
==> e%5E%28-lambda%29+=+0.264 ==> lambda+=+1.331806176
==> p%281%29+=+1.331806176%2Ae%5E%28-1.331806176%29+=+0.352, to three decimal places
Also,
p%282%29+=+%281.331806176%5E2%2F2%21%29%2Ae%5E%28-1.331806176%29+=+0.234, to three decimal places.
==> p(x > 2) = 1 - p(0) - p(1) - p(2) = 1 - 0.264 - 0.352 - 0.234 = 0.15.